The DOI matches its Crossref record; 36 of the 36 references it cites were found in a registry or an index.
Approximation of nonlinear systems with radial basis function neural networks
Abstract
A technique for approximating a continuous function of n variables with a radial basis function (RBF) neural network is presented. The method uses an n-dimensional raised-cosine type of RBF that is smooth, yet has compact support. The RBF network coefficients are low-order polynomial functions of the input. A simple computational procedure is presented which significantly reduces the network training and evaluation time. Storage space is also reduced by allowing for a nonuniform grid of points about which the RBFs are centered. The network output is shown to be continuous and have a continuous first derivative. When the network is used to approximate a nonlinear dynamic system, the resulting system is bounded-input bounded-output stable. For the special case of a linear system, the RBF network representation is exact on the domain over which it is defined, and it is optimal in terms of the number of distinct storage parameters required. Several examples are presented which illustrate the effectiveness of this technique.
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Cites
Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Multilayer feedforward networks are universal approximators
HornikK., StinchcombeM., & WhiteH. (1989) · Neural Networks · doi:10.5555/70405.70408 · Cited by 9,081
Identification and control of dynamical systems using neural networks
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Hornik, K. (1991) · Neural Networks · doi:10.1016/0893-6080(91)90009-t · Cited by 6,091
On the approximate realization of continuous mappings by neural networks
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Universal Approximation Using Radial-Basis-Function Networks
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An Introduction to Kolmogorov Complexity and Its Applications
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Orthogonal least squares learning algorithm for radial basis function networks
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Networks for approximation and learning
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Metadata
- Authors
- Schilling, R. J., Carroll, J. J., & Al-Ajlouni, A. F.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 2001
- Volume
- 12
- Issue
- 1
- Pages
- 1-15
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W2139704022
- Cited by
- 263
- References
- 36
- FWCI
- 5.63
- Type
- journal article
- Language
- en
- Open access
- closed
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